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Geometric growth and character development in large metastable networks

: Eggeling, Eva; Barmak, Katayun; Emelianenko, Maria; Epshteyn, Yekaterina; Kinderlehrer, David; Ta'asan, Shlomo

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Rendiconti di matematica e delle sue applicazioni 29 (2009), No.1, pp.65-81
ISSN: 1120-7183
ISSN: 0034-4427
Journal Article, Electronic Publication
Fraunhofer IGD ()
Fraunhofer Austria ()
material research; texture; growth process; topology

Cellular networks are ubiquitous in nature. They exhibit behavior on many different length and time scales and are generally metastable. Most technologically useful materials are polycrystalline microstructures composed of a myriad of small monocrystalline grains separated by grain boundaries. The energetics and connectivity of the grain boundary network plays a crucial role in determining the properties of a material across a wide range of scales. A central problem in materials science is to develop technologies capable of producing an arrangement of grains - a texture - that provides for a desired set of material properties.
Here we discuss briefly the role of energy in texture development, measured by a character distribution, and how this is different from the evolution of geometric features, which we term geometric coarsening. For this purpose we present a critical event model to deepen our understanding of the topological reconfigurations that occur during the growth process.